An absence of frequency spectrum bands that can support wide transmission bandwidths gives rise to intra-band or inter-band aggregation of multiple carriers according to specific sets of technical requirements. Such carrier aggregated signals have characteristics, such as high peak to average power ratio (PAPR), also commonly referred to as crest factor (CF), and wide bandwidth. The amplification of these carrier aggregated signals by a single power amplifier (PA) poses several challenges. A PA is required to maintain good power efficiency over multiple frequency bands. This has motivated recent research attempts to develop high efficiency, multiband and broadband devices such as Doherty PAs and envelope tracking systems. In addition, due to the high CF of the carrier aggregated signals, these PAs are often required to operate in the large back off region from their peak power to meet linearity requirements. Consequently, these PAs yield poor power efficiency.
Several techniques have been devised for crest factor reduction (CFR) of single band signals and consequently enhance PA efficiency and reduce the dynamic-range requirement imposed on digital to analog converters. These techniques can be divided into two categories: distortion-less methods (commonly called linear CFR techniques), such as selected mapping, partial transmit sequence, tone injection, tone reservation, and coding; and distortion-based methods (also called nonlinear CFR techniques) such as clipping/windowing, companding, active constellation extension (ACE), and generalized ACE methods.
Linear techniques can achieve greater CF reduction than their nonlinear counterparts without altering signal quality. However, linear techniques usually require modifications to the receiver that may be incompatible with existing communication systems. Linear techniques have been applied to multicarrier/single-standard signals through proper modulation and coding. However, the generalization of linear techniques to carrier aggregated signals is not possible due to the dissimilarity between the modulation schemes employed in each carrier.
The nonlinear CFR techniques are generally carefully applied to obtain the highest possible CF reduction while not exceeding the distortion threshold. These techniques, and in particular, the clipping/windowing technique, have been applied to multi-carrier signals co-located in the same spectrum band. However application of clipping/windowing techniques to carrier aggregated signals, especially when each carrier is located in different and widely spaced frequency bands, is very challenging because the clipping/windowing techniques may require very high, and thus, impractical sampling rates.
A carrier aggregated signal over two bands, such as shown in FIG. 1, can be expressed asx(t)=x1(t)+x2(t)={tilde over (x)}1(t)ejω1t+{tilde over (x)}2(t)ejω2t  (1)where x(t) is the carrier aggregated signal, x1(t) and x2(t) are the mixed mode signals in each band, and {tilde over (x)}1(t) and {tilde over (x)}2(t) denote the baseband envelopes of x1(t) and x2(t) around the angular frequencies ω1 and ω2, respectively. As shown in FIG. 1, the individual signals x1(t) and x2(t) have bandwidths B1 and B2, respectively, and are separated by a frequency gap S.
The carrier aggregated signal can be represented as a broadband signal with an angular carrier frequency
  (                    ω        1            +              ω        2              2    )as given by:
                                                                        x                ⁡                                  (                  t                  )                                            =                            ⁢                                                                    x                    1                                    ⁡                                      (                    t                    )                                                  +                                                      x                    2                                    ⁡                                      (                    t                    )                                                                                                                          =                            ⁢                                                                    x                    ~                                    ⁡                                      (                    t                    )                                                  ·                                  ⅇ                                      j                    ⁢                                                                                            ω                          1                                                +                                                  ω                          2                                                                    2                                        ⁢                    t                                                                                                                          =                            ⁢                                                (                                                                                                                                          x                            ~                                                    1                                                ⁡                                                  (                          t                          )                                                                    ⁢                                              ⅇ                                                  j                          ⁢                                                                                                                    ω                                1                                                            -                                                              ω                                2                                                                                      2                                                    ⁢                          t                                                                                      +                                                                                                                        x                            ~                                                    2                                                ⁡                                                  (                          t                          )                                                                    ⁢                                              ⅇ                                                  j                          ⁢                                                                                                                    ω                                2                                                            -                                                              ω                                1                                                                                      2                                                    ⁢                          t                                                                                                      )                                ⁢                                  ⅇ                                      j                    ⁢                                                                                            ω                          1                                                +                                                  ω                          2                                                                    2                                        ⁢                    t                                                                                                          (        2        )            where {tilde over (x)}(t) is the baseband envelope of the carrier aggregated signal. The baseband envelope, x(t), can be amplified using a dual-band or broadband PA instead of two single-band PAs in order to reduce a transmitter's cost and size. The carrier aggregation can result in an increased CF, which unless reduced, will require the designer to inefficiently operate the dual-band PA in its large back-off region.
The classical clipping/windowing nonlinear CFR technique can be applied to {tilde over (x)}(t). In such case the CFR module may be a single-input single-output (SISO) unit that processes a digitized version of x(t) which is sampled at a frequency f′s, where f′s≧2·(S+max(B1/2, B2/2)), and S, B1 and B2 represent the frequency spacing and the bandwidths of the two signals, respectively. The digitized baseband signal {tilde over (x)}(n′) can then be expressed as follows:
                                          x            ~                    ⁡                      (                          n              ′                        )                          =                                                                              x                  ~                                1                            ⁡                              (                                  n                  ′                                )                                      ⁢                          ⅇ                              j                ⁢                                                                            ω                      1                                        -                                          ω                      2                                                        2                                ⁢                                                      n                    ′                                                        fs                    ′                                                                                +                                                                      x                  ~                                2                            ⁡                              (                                  n                  ′                                )                                      ⁢                          ⅇ                              j                ⁢                                                                            ω                      2                                        -                                          ω                      1                                                        2                                ⁢                                                      n                    ′                                                        fs                    ′                                                                                                          (        3        )            
The classical clipping/windowing method consists of monitoring the instantaneous amplitude of the signal envelope, and limiting it to a preset threshold to obtain the targeted CF. A device 10 for implementing the classical clipping/windowing method is shown in FIG. 2. As can be seen, in addition to the clipping 12 and filtering modules 14, the SISO CFR of FIG. 2 includes an up-sampler 16, a digital up-converter 18, a down-sampler 20 and a down-converter 22. As this technique is a nonlinear operation, inband distortions and out of band spectrum regrowth are induced. In order to achieve an acceptable adjacent channel power ratio (ACPR), the clipped signal is filtered. The clipping threshold is set so that the CF is reduced while conforming to error vector magnitude (EVM) and ACPR specifications.
The frequency spacing S between the two carriers is generally significantly greater than the bandwidths of x1(t) and x2(t), i.e. B1 and B2, especially in the case of inter-band aggregation scenarios. Hence, f′s would need to be considerably larger than the frequencies fs1 and fs2 needed to digitize {tilde over (x)}1(t) and {tilde over (x)}2(t), respectively (fs1≧2·B1, fs2≧2·B2) .
For example, assume a carrier aggregated signal is composed of a 15 MHz wide band code division multiple access (WCDMA) signal around 2.1 GHz and a 10 MHz long term evolution (LTE) signal centered in 2.4 GHz. For such a combination, the minimum theoretical sampling frequency f′s must be higher than 610 MHz. This sampling frequency is significantly higher than the sampling frequencies needed to represent the WCDMA and LTE signals individually. The direct application of the SISO clipping/windowing to {tilde over (x)}(n′) is thus seen to imply a high and impractical sampling rate. The high sampling rate requirement associated with the conventional clipping and windowing approach makes this solution sub-optimal in the context of inter-band carrier aggregated signals.